Data transmission system comprising a decision feedback equalizer and using partial-response techniques

ABSTRACT

A system for transmitting an n-level data signal (dk) at a given symbol rate 1/T comprises a data transmitter (1), a transmission channel (2) and a data receiver (3) with an equalizer (30) of the decision feedback type. By arranging this equalizer (30) for forming an estimate ( @k) of a virtual m-level data signal (ck) instead of the output signal (bk) of the data transmitter (1) error propagation in the equalizer (30) is considerably reduced without thereby appreciably adding to the implementation-complexity of the system.

This is a continuation of application Ser. No. 203,655, filed June 7,1988, U.S. Pat. No. 4,866,736.

BACKGROUND OF THE INVENTION

The invention relates to a system for transmitting an n-level datasignal at a given symbol rate 1/T. This system being including by a datatransmitter with a data signal source, a transmission channel and a datareceiver with an equalizer of the decision feedback type, whichequalizer comprises a feedforward filter connected between the input ofthe data receiver and a first input of a difference circuit, a symboldecision circuit connected to the output of the difference circuit, anda feedback filter connected between the output of the symbol decisioncircuit and a second input of the difference circuit, in which thelinear part of the transmission path between the output of the datasignal source and the first input of the difference circuit can bedescribed by a linear signal transformation L.

Such a system is generally known and is described, for example, in thebook "Digital Communications" by J. G. Proakis, McGraw-Hill, 1983,Chapter 6, Section 6.5, pp. 382-386. In such systems the feedforwardfilter belonging to the equalizer provides for suppression of noise andcancellation of pre-cursive intersymbol interference (ISI), whilstpost-cursive intersymbol interference (ISI) is cancelled with the aid ofthe feedback filter synthesizing a replica of this interference on thebasis of the symbol decisions already formed, by which replica issubtracted from the output signal of the feedforward filter. In thesystem known from the book by Proakis the equalizer is arranged forforming at the input of the symbol decision circuit an estimate of adata signal generated by the data transmitter. Normally, this estimaterelates to the original n-level data signal, but in the case when thedata transmitter includes a linear encoder, it is likewise possible tohave this estimate relate to the output signal of the encoder andreconstruct in the data receiver the original n-level data signal fromthe symbol decisions formed then. The latter possibility occurs, forexample, in ISDN transmission systems in which pseudo-ternarytransmission codes are used, compare the article "A Baud-RateLine-Interface for Two-Wire High-Speed Digital Subscriber Loops" by C.A. Ehrenbard and M. F. Tompsett, Proc. GLOBECOM 1982, Miami, USA, pp. D.8.4.1-D.8.4.5, in which the use of a bipolar transmission code isdescribed.

In strongly dispersive transmission channels the output signal of thefeedforward filter shows a strongly post-cursive intersymbolinterference (ISI). Since the feedback filter has to synthesize areplica of this post-cursive ISI, erroneous symbol decisions applied tothe feedback filter will more seriously affect subsequent symboldecisions according as the transmission channel is more dispersive. Thisundesired continuing influence of erroneous symbol decisions is known aserror propagation and entails a degradation of the transmission quality,as appears, for example, from FIG. 6.5.2 on page 386 of the above bookby Proakis.

SUMMARY OF THE INVENTION

The invention has for its object to provide a novel concept of a systemof the type set forth in the preamble in which the said errorpropagation is reduced considerably without appreciably adding to theimplementation-complexity of the system.

Thereto, a system according to the invention is characterized in thatthe equalizer is arranged for forming at the input of the symboldecision circuit an estimate of a virtual m-level data signalcorrelating with the n-level data signal applied to the input of thelinear part of the transmission path according to a linear signaltransformation L_(v) which substantially characterizes the linear signaltransformation L and corresponds with a partial-response polynomialg_(v) (D) with D being a delay operator representing the symbol intervalT.

For completeness it should be observed that the m-level data signal tobe estimated is virtual if and only if g_(v) (D) ≠ 1, and if also g_(v)(D) ≠ g_(t) (D), where g_(t) (D) is the partial-response polynomialcorresponding with a linear signal transformation L_(t) optionallyperformed in the data transmitter.

The post-cursive ISI in the output signal of the feedforward filter issubstantially described by the linear signal transformation L_(v).According to the partial-response technique which is used in conformitywith the novel concept, the major part of this ISI may be considered tobe controlled desired ISI, so that only a small amount of undesiredresidual ISI remains which has to be cancelled by the feedback filter.The achieved reduction of the amplitude of the feedback filter outputsignal results in the erroneous symbol decisions applied to the feedbackfilter having a weaker strong influence on subsequent symbol decisions,therby achieving the intended reduction in error propagation.

An embodiment of the system according to the invention that isattractive with respect to its implementation is characterized in thatthe data transmitter comprises a precoder connected between the datasignal source and the input to the linear part of the transmission pathfor performing a non-linear signal transformation NL_(v) which isunambiguously determined by the linear signal transformation L_(v), inconformity with the partial-response technique, and in that the feedbackfilter in the data receiver is connected to the output of the symboldecision circuit through a decoder and a precoder which is identicalwith the precoder in the data transmitter, said decoder performing amemoryless inverse signal transformation L_(v) ⁻¹ ·NL_(v) ⁻¹ whichconverts the m-level symbol decisions into an n-level data signalcorresponding with the original n-level data signal. The precoderconnected to the decoder subsequently converts this n-level data signalinto a replica of the precoded n-level data signal generated in the datatransmitter applied to the input to the linear part of the transmissionpath. In this way the condition generally to be imposed on decisionfeedback equalization that the input signal of the feedback filter islinearly related to the output signal of the feedforward filter issatisfied. Besides, an n-level data signal is applied to the feedbackfilter, and because n is smaller than m, a digital implementation ofthis filter is thus simpler than when the formed m-level symboldecisions are applied directly.

A further advantage of this embodiment is the possibility of adaptivelyadjusting the feedback filter and also the feedforward filter in thedata receiver of the system under control of an error signal which canbe simply obtained and is representative of the difference between theinput signal of the symbol decision circuit and a symbol that can bederived from the input signal of the feedback filter by performing thelinear signal transformation L_(v).

This adaptive embodiment finally enables to further improve the alreadyachieved transmission quality by adding a relatively simple non-adaptivepost-detector to which the input signal of the symbol decision circuitis applied.

BRIEF DESCRIPTION OF THE DRAWING

The invention will be further explained hereinbelow with reference tothe drawing, in which:

FIG. 1 shows a block diagram of a conceptual embodiment of a datatransmission system in which the invention can be used;

FIG. 2 shows a functional discrete-time model of the system of FIG. 1when conventional measures are employed;

FIG. 3 shows a functional discrete-time model of the system of FIG. 1when the measures according to the invention are employed;

FIG. 4 shows a functional discrete-time model of an attractiveembodiment of a system according to the invention; and

FIG. 5 shows a functional discrete-time model of an adaptive embodimentof a receiver of a system according to the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

In FIG. 1 a block diagram is shown of a system for data signaltransmission with a data transmitter 1, a transmission channel 2 and adata receiver 3. The data transmitter 1 comprises a data signal source10 for generating a data signal. This data signal is converted by anencoder 11 into a data signal which is transmitted through transmissionchannel 2 at a symbol rate 1/T. The intersymbol interference (ISI) andnoise developed during this transmission are combated in the datareceiver 3. Thereto, data receiver 3 comprises an equalizer 30 of thedecision feedback type which includes a feedforward filter 31 which isdimensioned for suppressing in the best way possible pre-cursive ISI andnoise. On the basis of symbol decisions which are formed in a symboldecision circuit 32 a feedback filter 33 subsequently forms a cancellingsignal for post-cursive ISI which is subtracted from the output signalof feedforward filter 31 by means of a difference circuit 34 forobtaining the input signal of symbol decision circuit 32. Finally, fromthe formed symbol decisions a decoder 35 forms a replica of the originaldata signal which is applied to a data signal sink 36.

To illustrate the problem for which the invention provides a solution,FIG. 2 shows a functional discrete-time model of the system of FIG. 1when employing conventional measures. In the FIGS. 1 and 2 correspondingelements are denoted by the same reference symbols. The model of FIG. 2is given for the case in which data signal source 10 generates a binarydata signal and data transmitter 1 applies a ternary data signal totransmission channel 2.

A binary data signal d_(k) generated by data signal source 10 isconverted by a non-linear part 12 of the encoder 11 into a likewisebinary data signal a_(k) which, subsequently, by the linear part 13 ofthe encoder 11 is converted into a ternary data signal b_(k) to beapplied to discrete-time transmission channel 2. To characterize theoperation performed in this linear part 13 a partial-response polynomialg_(t) (D) can be used, D being a delay operator representing the symbolinterval T. Further details about these partial-response polynomials areto be found, for example, in the article "Partial-Response Signaling" byP. Kabal and S. Pasupathy, IEEE trans. Commun., Vol. COM-23, No. 9, pp.921-934, Sept. 1975. For explaining the following description it shouldbe observed that such polynomials generally have a relatively low orderand also, apart from an otherwise unimportant scale factor, only haveintegral-valued coefficients. In the present case, for the purpose ofillustration, the bipolar response 1-D for the polynomial g_(t) (D) ischosen such that

    b.sub.k =a.sub.k -a.sub.k-1.                               (1)

The ternary data signal b_(k) is converted into an output signal r_(k)by the cascade arrangement of transmission channel 2 and feedforwardfilter 31 in FIG. 1 according to

    r.sub.k =(b*(f*w)).sub.k +(n*w).sub.k,                     (2)

where the symbol"*" denotes the linear convolution-operator, f_(k) andw_(k) represent the discrete-time impulse responses of transmissionchannel 2 and feedforward filter 31, respectively, and n_(k) representsan additive discrete-time noise signal which is added by means of asummator 20.

With a proper dimensioning of the feedforward filter 31 of FIG. 1 itholds that the signal r_(k) contains virtually only post-cursive ISI.This implies that (f_(*) w)_(k) can significantly differ from zero onlyfor non-negative instants k. In the present system post-cursive ISI iscombated by making feedback filter 33 have a causal impulse responsep_(k) for which holds ##EQU1## and applying to this feedback filter 33the symbol decisions b_(k) which are formed by decision circuit 32. As aresult of the causal character of feedback filter 33 its output signalis at any instant k only determined by symbol decisions b_(k-i) with i≧1that have already been formed. Under normal operating conditions thesesymbol decisions are correct, so that the output signal of the feedbackfilter 33 can be described as

    (b*p).sub.k =(b*p).sub.k.                                  (4)

The output signal b_(k) of difference circuit 34 can now be described as

    b.sub.k =r.sub.k- (b*p).sub.k.                             (5)

In the case in which signal r_(k) only contains post-cursive ISI, thisformula when utilizing formulas (2), (3) and (4) can be simplified to

    b.sub.k =b.sub.k +(n*w).sub.k =b.sub..sub.k +n.sub.k ',    (6)

where n'_(k) represents the version of noise signal n_(k) that isattennuated in amplitued by feedforward filter 31. According to thelatter formula, in the absence of error propagation, at the input ofsymbol decision circuit 32 an ISI-free estimate b_(k) is formed of thedata signal b_(k) at the output of data transmitter 1.

For strongly dispersive transmission channels 2 the output signal offeedforward filter 31 usually shows a strongly postcursive ISI becausethe impulse response (f_(*) w)_(k) for k≧1 significantly differs fromzero. Consequently, the impulse response p_(k) of feedback filter 33according to formula (3) will also assume values significantly differingfrom zero for k≧1. This will unavoidably cause a relatively large effectof erroneous symbol decisions b_(k-1) with i≧1 that have already beenformed on symbol decisions b_(k+i) with i≧0 that still have to beformed.

In FIG. 2 the cascade arrangement of the linear part 13 of encoder 11 indata transmitter 1, the transmission channel 2 and the feedforwardfilter 31 of equalizer 30 in data receiver 3 constitutes the linear partof the transmission path between the output of data signal source 10 andthe first input of difference circuit 34. The operation of this cascadearrangement (13, 2, 31) can be described by a linear signaltransformation L, as is symbolically shown in FIG. 2. Instead ofinserting summator 20 at the input of feedforward filter 31 in thiscascade arrangement (13, 2, 31) it is equally possible to insert same atthe output of this feedforward filter 31 having impulse response w_(k).On the basis of the above considerations it will be evident that in thelatter case summator 20 has to add to the output signal of this cascadearrangement (13, 2, 31) an additive noise signal (n_(*) w)_(k) in orderto produce the same signal r_(k) at the first input of differencecircuit 34 as in the case shown in FIG. 2.

The latter option is used for elucidating the description of FIG. 3showing a functional discrete-time model of the system of FIG. 1 whenutilizing the measures according to the invention. In the FIGS. 1, 2 and3 corresponding elements are denoted by the same reference symbols.

The linear part 13 of encoder 11 in FIG. 3 again performs an operationwhich is characterized by the partial-response polynomial g_(t) (D)=1-D.At the output of data transmitter 1 in FIG. 3 then again a ternary datasignal b_(k) according to formula (1) will occur

    b.sub.k =a.sub.k -a.sub.k-1                                (7)

and at the first input of difference circuit 34 in data receiver 3 asignal r_(k) according to formula (2)

    r.sub.k =(b*(f*w)).sub.k +(n*w).sub.k.                     (8)

In many cases it is possible to present a relatively simplepartial-response polynomial g_(c) (D) such that the associated impulseresponse g_(c),k --which is built up out of the respective coefficientsof the polynomial --forms a proper styling of the impulse response(f_(*) w)_(k) of the cascade arrangement of transmission channel 2 andfeedforward filter 31. This implies that the linear signaltransformation corresponding with the impulse response (f_(*) w)_(k)representative of the overall linear transmission distortion can beconsidered to be built up as a sequence of partial-responsetransformation L_(c) which corresponds with g_(c) (D), and a residualtransformation L_(r) which takes into account the generally minor effectof the residual linear transmission distortion. In the present example,the duobinary response 1+D is taken for g_(c) (D), which response isillustrative of many transmission channels 2 having a low-pass charactersuch as, for example, ISDN connections in the local public telephonenetwork. This conceptual splitting-up is expressed in FIG. 3 by apartial-response circuit 21 corresponding with linear signaltransformation L_(c) and having an impulse response g_(c),k' whichcircuit 21 is followed by a residual circuit 22 corresponding withlinear signal transformation L_(r) and having an impulse response h_(k).In partial-response circuit 21 ternary data signal b_(k) at the outputof data transmitter 1 is converted into a virtual m-level data signalc_(k) (signal c_(k) is a "virtual" signal because it is not explicitlyvisible at any point between the in and output of the physicaltransmission channel 2). Then, for this m-level data signal c.sub. k itholds that

    c.sub.k =(b*g.sub.c).sub.k,                                (9)

which expression for the assumed duobinary response g_(c) (D)=1+D issimplified to

    c.sub.k =b.sub.k +.sub.k-1.                                (10)

On the basis of formula (7) it then follows that c_(k) is related tobinary data signal a_(k) at the input of linear part 13 of encoder 11 indata transmitter 1 according to

    c.sub.k =a.sub.k -a.sub.k-2,                               (11)

so that c_(k) in this case is a ternary data signal (thus m=3). Thisrelationship can be described by a linear signal transformation L_(v)which can be assumed to be built up as a sequence of partial-responsetransformations L_(t) and L_(c) which correspond with the polynomialsg_(t) (D) and g_(c) (D), as represented in FIG. 3. The signaltransformatiON L_(v) then corresponds with a partial-response polynomialg_(v) (D) for which holds

    g.sub.v (D)=g.sub.t (D)·g.sub.c (D).              (12)

In the present example the bipolar response 1-D is chosen for g_(t) (D)and the duobinary response 1+D for g_(c) (D), so that

    g.sub.v (D)=(1-D)(1+D)=1-D.sup.2.                          (13)

In view of the generally relatively small residual transmissiondistortion which is represented by the impulse response h_(k), thesignal transformation L of the linear part (13, 2, 31) of thetransmission path between the output of signal source 10 and the firstinput of difference circuit 34 is substantially characterized by thelinear signal transformation L_(v) which is performed by the cascadearrangement of linear part 13 of encoder 11 and partial-response circuit21.

The described conceptual splitting-up becomes explicitly visible in datareceiver 3 of FIG. 3 because in accordance with the invention equalizer30 is arranged for forming at the input of symbol decision circuit 32 anestimate c_(k) of the virtual data signal c_(k) instead of an estimateb_(k) of the data signal b_(k) at the output of data transmitter 1. Thetask to be performed by the equalizer 30 is less exacting in the case ofFIG. 3 in view of the relatively small residual transmission distortionwhich is represented by the impulse response h_(k). This can be shown bya further analysis of the model of FIG. 3. As appears from thesplitting-up of FIG. 3 the signal r_(k) at the first input of differencecircuit 34 can be written as

    r.sub.k =(c*h).sub.k +(n*w).sub.k.                         (14)

By analogy with the foregoing, under normal operational conditions thealready formed symbol decisions c_(k-i) with i≧1 may be assumed to becorrect. Applying these correct symbol decisions to feedback filter 33,now having an impulse response q_(k), then results in an output signal

    (c*q).sub.k =(c*q).sub.k.                                  (15)

By utilizing formulas (14) and (15) it now appears that at the input ofsymbol decision circuit 32 a signal c_(k) develops having the form

    c.sub.k =(c*h).sub.k -(c*q).sub.k +(n*w).sub.k.            (16)

In order to let this signal c_(k) be as good an approximation aspossible of the virtual data signal c_(k), it is necessary according tothis formula that the impulse response q_(k) of feedback filter 33 be afaithful copy of the causal part of the impulse response h_(k), that isto say ##EQU2## As appears from the foregoing, impulse response h_(k)usually represents only a small amount of linear transmissiondistortion, so that the impulse response q_(k) will take on relativelysmall values, and already formed erroneous symbol decisions c_(k-i) withi≧1 only affect to a limited extent the symbol decisions c_(k+i) withi≧0 still to be formed.

The reduction of error propagation achieved thus can be aptlyillustrated with reference to the situation in which no residual lineartransmission distortion occurs, so that

    h.sub.k =δ.sub.k,                                    (18)

where δ_(k) represents the Kronecker delta function. The linear signaldistortion introduced by the cascade arrangement of transmission channel2 and feedforward filter 31 can then be characterized exactly in bothFIG. 2 and FIG. 3 by the partial-response transformation L_(c), so that

    (f*w).sub.k =g.sub.c,k.                                    (19)

According to the conventional approximation of FIG. 2 the impulseresponse p_(k) according to formula (3) is a replica of the part withk≧1 of (f*w)_(k), that is to say ##EQU3## For the chosen duobinaryresponse g_(c) (D)=1+D it holds that g_(c),1 =1 and g_(c),k =0 for k≧2,so that the first coefficient of the feedback filter 33 has a largenon-zero value which may lead to significant error propagation.Conversely, the approximation according to the invention results in afeedback filter 33 whose impulse response q_(k) is a replica of the partwith k≧1 of the impulse response h_(k), which part according to formula(18) is equal to zero for all k≧1. Consequently, all coefficients offeedback filter 33 are also equal to zero, so that error propagation iseliminated completely. It will be evident that this ideal situation, inwhich a feedback filter 33 is actually redundant, will not occur inpractice. However, in general it will still hold that the firstcoefficients q_(k) according to FIG. 3 then have a considerably smalleramplitude than the corresponding first coefficients p_(k) according toFIG. 2, so that error propagation is accordingly smaller.

In the configuration as shown in FIG. 3 an m-level signal c_(k) isapplied to feedback filter 33, where m=3 for the present example withg_(v) (D)=1-D². By carrying out in encoder 11 of data transmitter 1 asuitable non-linear signal transformation NL_(v), it is possible toreduce this number of m signal levels and thus simplify a digitalimplementation of feedback filter 33.

This possibility is represented in FIG. 4 showing a functionaldiscrete-time model of a system according to the invention. In the FIGS.3 and 4 corresponding elements are denoted by the same referencesymbols.

In addition to the said non-linear signal transformation NL_(v) othernon-linear signal processes too can generally take place in thenon-linear part 12 of encoder 11. To simplify the following descriptionthese other non-linear signal processes are assumed to be incorporatedin data signal source 10.

As explained hereinbefore, the operation of, equalizer 30 according tothe invention is aimed towards combatting the residual lineartransmission distortion which is represented by the impulse responseh_(k). Consequently, with a proper functioning of equalizer 30 therelation between the data signal a_(k) at the input of the linear part(13, 21, 22) of the transmission path and the input signal c_(k) ofsymbol decision circuit 32 can also be characterized by the linearsignal transformation L_(v). Since this linear signal transformationL_(V) in its turn is characterized by a partial-response polynomialg_(v) (D), according to the said article by Kabal and Pasupathy there isa non-linear signal transformation NL_(v) denoted "precoding" and havingthe feature that the sequence of the inverse operations L_(v) ⁻¹ andNL_(v) ⁻¹ of L_(v) and NL_(v), respectively, is a simple memorylessinverse signal mapping (MIM) which can be symbolically denoted L_(v) ⁻¹·NL_(v) ⁻¹. By using this precoding NL_(v) in the non-linear part 12 ofencoder 11 it is achieved that from the formed symbol decisions c_(k) adirect estimate d_(k) of input signal d_(k) of encoder 11 can beobtained by carrying out this memoryless inverse signal mapping MIM indecoder 35. By applying the data signal d_(k) obtained thus to aprecoder 37 which is identical with precoder 12 in data transmitter 1,an estimate a_(k) is obtained of data signal a_(k) at the input of thelinear part (13, 21, 22) of the transmission path and this estimatea_(k) is applied to feedback filter 33. Thus, the condition generally tobe imposed on the decision feedback equalization that the input signalof feedback filter 33 be linearly related to the signal at the firstinput of difference circuit 34 is satified. Since the precoded datasignal a_(k) has the same number of n amplitude levels as the originaldata signal d_(k), a digital implementation of feedback filter 33 issimpler in FIG. 4 than in FIG. 3, in which a data signal with m>namplitude levels is applied to feedback filter 33. In the presentexample with g_(v) (D)=1-D² not a ternary, but a binary data signal isapplied to feedback filter 33.

As appears from the foregoing, there is a relationship between the datasignals c_(k) and a_(k) that can be characterized by the linear signaltransformation L_(v). Therefore, in absence of erroneous symboldecisions c_(k) the same holds for the relationship between the datasignals c_(k) and a_(k) of FIG. 4. Expressed in a formula this meansthat

    c.sub.k =(a*g.sub.v).sub.k.                                (21)

In order to realize the same output signal of the feedback filter 33 inthe configuration of FIG. 4 as in FIG. 3, feedback filter 33 in FIG. 4has to have an impulse response q_(k) ', so that

    (a*q').sub.k =(c*q).sub.k.                                 (22)

On the basis of the relationship between the data signals c_(k) anda_(k) according to formula (21), q_(k) ' has to be related to q_(k)according to formula (22) as

    q.sub.k '=(q*g.sub.v).sub.k.                               (23)

The convolution in formula (23) generally has a shortening effect on theimpulse response of feedback filter 33, as will now be explained.

In the absence of erroneous symbol decisions data signal c_(k) at theoutput of symbol decision circuit 32 has a controlled ISI structurewhich is characterized by the linear signal transformation L_(v). Forthe prevailing partial-response transformations L_(v) this structureleads to zeros in the amplitude spectrum of data signal c_(k), whichzeros are often situated at the frequency 0 and/or at the Nyquistfrequency 1/(2T).

As the above has shown, feedback filter 33 should cancel a residualtransmission distortion which is represented by the impulse responseh_(k). The desired feedback filter output signal defined well in thismanner has to be generated in FIG. 3 by a convolution of data signalc_(k) at its input and its impulse response q_(k). As the amplitudespectrum of this input signal c_(k) has zeros at frequencies determinedby L_(v), the transfer function of feedback filter 33 around thesefrequencies can be chosen freely without an appreciable effect on thedesired output signal. Especially with an adaptive adjustment offeedback filter 33 as shown in FIG. 3 this freedom may inadvertentlyresult in feedback filter 33 having a large transfer at the saidfrequencies determined by L_(v). Such a large transfer is attended withan impulse response q_(k) of feedback filter 33 which extends over alarge time span and/or has large amplitude values, and thus may lead toserious error propagation in both cases. According to formula (23)impulse response q_(k) ' of feedback filter 33 in FIG. 4 is determinedby the convolution of the impulse response g_(v),k, which itself isdetermined by the linear signal transformation L_(v), and the justdescribed impulse response q_(k) of feedback filter 33 in FIG. 3. Thus,it is achieved that a possible large transfer of feedback filter 33 inFIG. 3 at the said frequencies determined by L_(v) is cancelledcompletely or substantially completely in FIG. 4 by the very smalltransfer at these same frequencies of the impulse response g_(v),klikewise determined by L_(v). Consequently, the impulse response q_(k) 'of feedback filter 33 in FIG. 4 will extend over a considerably smallertime span and/or have considerably smaller amplitude values than theimpulse response q_(k) of feedback filter 33 in FIG. 3, thusconsiderably reducing the risk of error propagation.

It will be evident that this advantage of reduced error propagation indata receiver 3 as shown in FIG. 4 is maintained if instead of virtualdata signal c_(k) the actually transmitted data signal b_(k) isreconstructed by symbol decision circuit 32. Even then the configurationas shown in FIG. 3, in which symbol decisions b_(k) with respect toactually transmitted data signal b_(k) are applied directly to feedbackfilter 33, could, according to the just described mechanism, lead to animpulse response q_(k) of feedback filter 33 extending over a large timespan and/or having large amplitude values. Thus, serious errorpropagation may occur. In the configuration as shown in FIG. 4 thecorresponding impulse response q_(k) ' of feedback filter 33 leads,under the same circumstances, to a considerably smaller errorpropagation owing to the convolution of impulse response q_(k) and theimpulse response g_(t),k corresponding with linear signal transformationL_(t) which is performed in linear part 13 of encoder 11 in datatransmitter 1.

As explained hereinbefore, the advantages of a simplified implementationof feedback filter 33 and reduced error propagation realized by means ofthe configuration of FIG. 4 apply both in the case where at the input ofsymbol decision circuit 32 an estimate c_(k) of virtual data signalc_(k) is formed and in the case where an estimate b_(k) of actuallytransmitted data signal b_(k) is formed. Since these data signals c_(k)and b_(k), respectively, are related to data signal a_(k) at the inputof the linear part (13, 21, 22) of the transmission path via the linearsignal transformations L_(v) =L_(t) ·L_(c) and L_(t), respectively, itis evident that said two advantages generally occur if at the input ofsymbol decision circuit 32 an estimate is formed of an m-level datasignal that is related to n-level data signal a_(k) according to alinear signal transformation L with L=L_(v) or L=L_(t), which linearsignal transformation L corresponds with a partial-response polynomialg(D)=g_(v) (D) and g(D)=g_(t) (D), respectively.

An additional advantage of the configuration of data receiver 3 shown inFIG. 4 relates to the option of adaptively implementing feedback filter33 and possibly also feedforward filter 31. This option is illustratedin FIG. 5.

In FIG. 5, both filters 31 and 33 now comprise an adaptation circuit31(a) and 33(a), respectively, arranged according to conventionaltechniques. These adaptation circuits 31(a) and 33(a) are controlled bythe same error signal ε_(k) which is representative of the differencebetween input signal c_(k) of symbol decision circuit 32 and a datasignal c_(k) '. This data signal c_(k) 'is derived in a simple way fromthe input signal a_(k) of feedback filter 33 by means of apartial-response circuit 38 in which the desired partial-responsetransformation L_(v) is effected. By means of a difference circuit 39the difference Δ_(k) between the signals c_(k) 'and c_(k) ' is formed,and in FIG. 5 this difference Δ_(k) is used directly as error signalε_(k). As is well known, in adaptive filters prescribed functions ofΔ_(k), such as, for example, strongly quantized versions of Δ_(k), canbe used as error signal ε_(k) in order to simplify their digitalimplementation. When using the error signal ε_(k) thus obtained it isachieved in a simple manner that, after convergence of the adaptivefilters 31 and 33, the data component c_(k) -(n_(*) w)_(k) of the inputsignal c_(k) of symbol decision circuit 32 is related in the desiredmanner to the data signal a_(k) at the output of precoder 12 in datatransmitter 1, that is to say, via the desired linear signaltransformation L_(v) embedded in partial-response circuit 38. Theapparently more obvious implementation, in which the in and outputsignals c_(k) and c_(k) of symbol decision circuit 32 are used directlyfor forming the error signal ε_(k), true enough, also results in alinear relationship between the data component c_(k) -(n_(*) w)_(k) ofc_(k) and the data signal a_(k) after adaptation of filters 31 and 33,but inevitably leads to the problem that it cannot be predicted a prioriwhich linear relationship exactly will be established, so that anundesired adjustment of equalizer 30 cannot be precluded in advance.

It is evident that the latter advantage of a predictable convergencebehaviour is maintained if a desired linear signal transformationL=L_(t) instead of a desired linear signal transformation L=L_(v) isperformed in partial-response circuit 38. As already explainedhereinbefore, this linear signal transformation L=L_(t) leads to symboldecisions b_(k) of actually transmitted data signal b_(k), so that inthis case decoder 35 has to perform a memoryless inverse mapping L⁻¹·NL⁻¹ =L_(t) ⁻¹ ·NL_(t) ⁻¹ , whilst precoder 37 has to carry out theassociated non-linear signal transformation NL=NL_(t).

The predictable convergence behaviour of feedforward filter 31 andfeedback filter 33 which is garanteed by partial-response circuit 38 inFIG. 5 leads to an input signal c_(k) of symbol decision circuit 32 witha correlation structure substantially corresponding with thewell-defined correlation structure of output signal c_(k) ' ofpartial-response circuit 38, which correlation structure can becharacterized by a partial-response polynomial g_(v) (D) or g_(t) (D).This well-defined correlation structure of input signal c_(k) of symboldecision circuit 32 in FIG. 5 can now be used for realizing a furtherimprovement of transmission quality by adding a non-adaptivepost-detector 40 for forming final symbol decisions d_(k-M) which areapplied to a data signal sink 36', as shown in FIG. 5 by way of a dashedline. Such a post-detector is known from an article "Maximum-LikelihoodSequence Estimation of Digital Sequences in the Presence of IntersymbolInterference" by G. D. Forney, Jr., published in IEEE Trans. Inform.Theory, Vol. IT-18, No. 3, pp. 363-378, May 1972. In this article anon-adaptive detector is described which is arranged for estimating themaximum-likeihood sequence of transmitted data symbols d_(k) and theretomakes optimum use of the correlation structure of its input signalc_(k). This leads to a transmission quality which is better than whenmaking symbol-by-symbol decisions as performed in symbol decisioncircuit 32. For correlation structures of the partial-response typeconsidered, according to the article by Forney improvements oftransmission quality corresponding with an improvement of 2-3 dB in thesignal-to-noise ratio are often obtainable in this manner. In addition,the implementation of non-adaptive post-detector 40 can remainrelatively simple as a result of the low order and the resulting shortmemory span of the partial-response polynomial (g_(v) (D) or (g_(t) (D))which determines the correlation structure of input signal c_(k) ofpost-detector 40. Needless to observe that also different types ofnon-adaptive detectors exploiting this well-defined correlationstructure for achieving an improved transmission quality can be used aspost-detector 40 in FIG. 5. It will also be evident after the aboveexplanation that in the non-adaptive configurations of the FIGS. 2, 3and 4 it may be sensible to connect such a non-adaptive post-detector tothe input of symbol decision circuit 32 for forming final symboldecisons d_(k-M) having a better quality than the decisions d_(k), butfor simplicity, this option has not been shown any further in theseFigures.

What is claimed is:
 1. A data receiver comprising(a) an input; and (b) adecision feedback equalizer which includes:(i) a difference circuithaving first and second inputs and an output; (ii) a feedforward filtercoupled between the input of the data receiver and the first input ofthe difference circuit and incorporated in a linear part of atransmission path, which part is described by a linear signaltransformation L, to which part is applied a derived n-level data signalderived from an original n-level data signal and having a symbol rate1/T; (iii) a feedback filter having an output coupled with the secondinput of the difference circuit; and (iv) a symbol decision circuithaving(A) an input coupled to the output of the difference circuit toreceive therefrom an estimate of an m-level data signal related to thederived n-level data signal according to a linear signal transformationL_(t), which substantially characterizes a linear portion of an encoderin a transmitter from which the original n-level signal originates,which transformation L_(t) corresponds with a partial-responsepolynomial g_(t) (D), with D being a delay operator representing thesymbol interval T; and (B) an output coupled with an input of thefeedback filter,where m and n are integers.
 2. The data receiver ofclaim 1 further comprising:(a) a decoder performing a memoryless inversesignal transformation L_(t) ⁻¹ ·NL_(t) ⁻¹ which converts m-level symboldecisions into an n-level data signal corresponding with the originaln-level data signal, the decoder having an input coupled with the outputof the symbol decision circuit; and (b) a precoder performing thenon-linear signal transformation NL_(t), which converts the n-level datasignal at an output of the decoder into an n-level data signalcorresponding to the derived n-level data signal; and wherein (c) thethe input of the feedback filter is coupled to the output of the symboldecision circuit through the decoder and the precoder.
 3. The datareceiver of claim 1 further comprising a post detector having an inputcoupled with the input of the symbol decision circuit for forming afinal estimate of the original n-level data signal.
 4. The data receiverof claim 2 further comprising a post detector having an input coupledwith the input of the symbol decision circuit for forming a finalestimate of the original n-level data signal.
 5. The data receiver ofclaim 1 further comprising:(a) a second difference circuit having firstand second inputs and an output, the first input being coupled with theinput of the symbol decision circuit and the output being coupled with asecond input of the feedback filter to provide thereto an error signal;and (b) means for performing the linear signal transformation L_(t), theperforming means having an input coupled with the input of the feedbackfilter and an output coupled with the second input of the seconddifference circuit; andwherein (c) the feedback filter adaptivelyadjusts under control of the error signal.
 6. The data receiver of claim5 wherein(a) the output of the second difference circuit is furthercoupled with a second input of the feedforward circuit; and (b) thefeedforward filter is adaptively adjusts under control of the errorsignal.
 7. The data receiver of claim 2 further comprising:(a) a seconddifference circuit having first and second inputs and an output, thefirst input being coupled with the input of the symbol decision circuitand the output being coupled with a second input of the feedback filterto provide thereto an error signal; and (b) means for performing thelinear signal transformation L_(t), the performing means having an inputcoupled with the input of the feedback filter and an output coupled withthe second input of the second difference circuit; and wherein (c) thefeedback filter adaptively adjusts under control of the error signal. 8.The data receiver of claim 7 wherein(a) the output of the seconddifference circuit is further coupled with a second input of thefeedforward circuit; and (b) the feedforward filter is adaptivelyadjusts under control of the error signal.
 9. The data receiver of claim3 further comprising:(a) a second difference circuit having first andsecond inputs and an output, the first input being coupled with theinput of the symbol decision circuit and the output being coupled with asecond input of the feedback filter to provide thereto an error signal;and (b) means for performing the linear signal transformation L_(t), theperforming means having an input coupled with the input of the feedbackfilter and an output coupled with the second input of the seconddifference circuit; and wherein (c) the feedback filter adaptivelyadjusts under control of the error signal.
 10. The data receiver ofclaim 9 wherein(a) the output of the second difference circuit isfurther coupled with a second input of the feedforward circuit; and (b)the feedforward filter is adaptively adjusts under control of the errorsignal.
 11. The data receiver of claim 4 further comprising:(a) a seconddifference circuit having first and second inputs and an output, thefirst input being coupled with the input of the symbol decision circuitand the output being coupled with a second input of the feedback filterto provide thereto an error signal; and (b) means for performing thelinear signal transformation L_(t), the performing means having an inputcoupled with the input of the feedback filter and an output coupled withthe second input of the second difference circuit; and wherein (c) thefeedback filter adaptively adjusts under control of the error signal.12. The data receiver of claim 11 wherein(a) the output of the seconddifference circuit is further coupled with a second input of thefeedforward circuit; and (b) the feedforward filter is adaptivelyadjusts under control of the error signal.